Problem: Simplify the following expression: $ y = \dfrac{-2q - 8}{10q + 5} - \dfrac{3}{7} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{-2q - 8}{10q + 5} \times \dfrac{7}{7} = \dfrac{-14q - 56}{70q + 35} $ Multiply the second expression by $\dfrac{10q + 5}{10q + 5}$ $ \dfrac{3}{7} \times \dfrac{10q + 5}{10q + 5} = \dfrac{30q + 15}{70q + 35} $ Therefore $ y = \dfrac{-14q - 56}{70q + 35} - \dfrac{30q + 15}{70q + 35} $ Now the expressions have the same denominator we can simply subtract the numerators: $y = \dfrac{-14q - 56 - (30q + 15) }{70q + 35} $ Distribute the negative sign: $y = \dfrac{-14q - 56 - 30q - 15}{70q + 35}$ $y = \dfrac{-44q - 71}{70q + 35}$